%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU224+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:08 PM UTC 2026
% Result : Theorem 1.15s 1.86s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 142 ( 28 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 176 ( 69 ~; 72 |; 23 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 70 ( 6 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l82_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
fof(t68_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
inference(assume_negation,[status(cth)],[l82_funct_1]) ).
fof(c_0_7,plain,
! [X100,X101,X102,X103] :
( ( relation_dom(X101) = set_intersection2(relation_dom(X102),X100)
| X101 != relation_dom_restriction(X102,X100)
| ~ relation(X102)
| ~ function(X102)
| ~ relation(X101)
| ~ function(X101) )
& ( ~ in(X103,relation_dom(X101))
| apply(X101,X103) = apply(X102,X103)
| X101 != relation_dom_restriction(X102,X100)
| ~ relation(X102)
| ~ function(X102)
| ~ relation(X101)
| ~ function(X101) )
& ( in(esk14_3(X100,X101,X102),relation_dom(X101))
| relation_dom(X101) != set_intersection2(relation_dom(X102),X100)
| X101 = relation_dom_restriction(X102,X100)
| ~ relation(X102)
| ~ function(X102)
| ~ relation(X101)
| ~ function(X101) )
& ( apply(X101,esk14_3(X100,X101,X102)) != apply(X102,esk14_3(X100,X101,X102))
| relation_dom(X101) != set_intersection2(relation_dom(X102),X100)
| X101 = relation_dom_restriction(X102,X100)
| ~ relation(X102)
| ~ function(X102)
| ~ relation(X101)
| ~ function(X101) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).
fof(c_0_8,plain,
! [X79,X80] :
( ( relation(relation_dom_restriction(X79,X80))
| ~ relation(X79)
| ~ function(X79) )
& ( function(relation_dom_restriction(X79,X80))
| ~ relation(X79)
| ~ function(X79) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(c_0_9,plain,
! [X71,X72] :
( ~ relation(X71)
| relation(relation_dom_restriction(X71,X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
fof(c_0_10,plain,
! [X62,X63,X64,X65,X66,X67,X68,X69] :
( ( in(X65,X62)
| ~ in(X65,X64)
| X64 != set_intersection2(X62,X63) )
& ( in(X65,X63)
| ~ in(X65,X64)
| X64 != set_intersection2(X62,X63) )
& ( ~ in(X66,X62)
| ~ in(X66,X63)
| in(X66,X64)
| X64 != set_intersection2(X62,X63) )
& ( ~ in(esk1_3(X67,X68,X69),X69)
| ~ in(esk1_3(X67,X68,X69),X67)
| ~ in(esk1_3(X67,X68,X69),X68)
| X69 = set_intersection2(X67,X68) )
& ( in(esk1_3(X67,X68,X69),X67)
| in(esk1_3(X67,X68,X69),X69)
| X69 = set_intersection2(X67,X68) )
& ( in(esk1_3(X67,X68,X69),X68)
| in(esk1_3(X67,X68,X69),X69)
| X69 = set_intersection2(X67,X68) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])]) ).
fof(c_0_11,negated_conjecture,
( relation(esk5_0)
& function(esk5_0)
& ( ~ in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0)))
| ~ in(esk4_0,relation_dom(esk5_0))
| ~ in(esk4_0,esk3_0) )
& ( in(esk4_0,relation_dom(esk5_0))
| in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))) )
& ( in(esk4_0,esk3_0)
| in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_12,plain,
( relation_dom(X1) = set_intersection2(relation_dom(X2),X3)
| X1 != relation_dom_restriction(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X60,X61] : set_intersection2(X60,X61) = set_intersection2(X61,X60),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_16,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0)))
| ~ in(esk4_0,relation_dom(esk5_0))
| ~ in(esk4_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]),c_0_14]) ).
cnf(c_0_20,negated_conjecture,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
function(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk4_0,set_intersection2(esk3_0,relation_dom(esk5_0))),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( in(esk4_0,esk3_0)
| in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(esk4_0,relation_dom(esk5_0))
| ~ in(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
in(esk4_0,esk3_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_20]),c_0_21])]),c_0_22]),c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( in(esk4_0,relation_dom(esk5_0))
| in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk4_0,relation_dom(esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
in(esk4_0,relation_dom(relation_dom_restriction(esk5_0,esk3_0))),
inference(sr,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_19]),c_0_22]),c_0_20]),c_0_21])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.20 % Problem : SEU224+1 : TPTP v9.2.1. Released v3.3.0.
% 0.03/0.20 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.43 % Computer : n025.cluster.edu
% 0.13/0.43 % Model : x86_64 x86_64
% 0.13/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.43 % Memory : 8042.1875MB
% 0.13/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.43 % CPULimit : 300
% 0.13/0.43 % WCLimit : 300
% 0.13/0.43 % DateTime : Tue May 5 02:49:58 EDT 2026
% 0.13/0.44 % CPUTime :
% 0.15/0.45 % start to proof: theBenchmark
% 1.15/1.86 % Version : CSE_E---1.7
% 1.15/1.86 % Problem : theBenchmark.p
% 1.15/1.86 % SZS status Theorem for theBenchmark.p
% 1.15/1.86 % SZS output start CNFRefutation
% See solution above
% 1.15/1.86 % Total time : 1.388s
%------------------------------------------------------------------------------